This invention relates generally to calculating credit migration for an obligor over a given time horizon and, more particularly, to network-based methods and systems for calculating an optimized transition probability matrix for more accurately predicting a likelihood that a credit rating of an obligor will migrate from one credit state to another credit state over a given time horizon.
Commercial lenders generally engage in the business of providing financing to individuals and other business entities, generally referred to as obligors, by using financial instruments that include standard loans as well as structured finance products and corporate bonds. Many of these obligors are assigned a letter-based rating grade or some other type of credit rating that is representative of the commercial obligors' credit worthiness. These credit rating grades for an obligor may shift, or migrate, over time as financial conditions associated with each obligor vary. For example, if a particular commercial obligor has an initial credit rating of AAA assigned via Standard and Poor's rating system, the credit rating may temporarily shift downward to a AA rating, and then return to a AAA rating thereafter over a certain time horizon. Also, for example, there may be a finite possibility that a commercial obligor with an initial credit rating of AAA may transition to a default rating over a certain time horizon. These credit rating shifts may result from changes in the financial condition of the obligor, changes in the financial conditions of the overall market or a combination of many financial factors. Also, a commercial lender will typically have a plurality of obligors in a portfolio.
Transition probability matrices (TPMs), which indicate a likelihood of an obligor's credit rating migrating from one credit state to another credit state over a given time horizon, have been used in various credit applications ranging from pricing of financial instruments, loan evaluation, portfolio risk analysis, and economic capital assessment. Typically, these TPMs are initially constructed from historical, or empirical credit ratings data. Moreover, the standard methodology for calculating TPMs includes using a discrete, cohort approach, and often employs using two assumptions that include, firstly, the TPMs follow a first-order Markov process, or Markov chain, and that, secondly, the data inherently includes a predetermined homogeneity.
In general, TPMs typically have a rectangular, tabular structure that is at least partially representative of a range of discrete credit ratings. Each credit rating includes an associated numerical value that is representative of an estimated future transition probability of a rating migration from a first credit rating to a second credit rating within the period the TPM was calculated for. Such a TPM also includes values that are representative of a probability of the associated obligor's credit rating remaining static in that period. Moreover, such a TPM likely includes a “default” state, wherein the default state indicates a probability that an obligor may default in that period on the associated financial instrument, or a plurality of instruments. Such an estimated default probability provides a lender with an estimated probability of default associated with a particular group of obligors. Specifically, a financial portfolio of all obligors, a financial portfolio of a particular group of obligors, or a financial portfolio of a single obligor is multiplied by a TPM to generate a risk forecast associated with the associated portfolio.
In addition, a range of estimated transition probabilities across a range of credit ratings provides some measure of estimated credit rating transition rates for a lender. These values provide commercial lenders with at least some data that can be used to predict whether a particular obligor will transition from one credit rating to another including a default credit rating so that the lender can decide whether to provide a particular financial instrument to the obligor, determine an extent of financing to be provided to the obligor, and determine a financing rate that is at least partially reflective of the associated risk.
Empirical TPMs, or ETPMs, are TPMs generated from empirical (i.e., known historical data) rating and rating transition data, and are published regularly by rating agencies over several years. These ETPMs are typically generated and published for a one-year forecast. Users of these ETPMs have tended to use these published matrices either directly, or after applying one of several smoothing techniques. A need for such smoothing is typically due to imprecise characteristics of empirical matrices that include a tendency for these ETPMs to be affected by idiosyncratic historical events, a sparse data population for plausible future scenarios, and/or vintage effects induced by the temporal location of the underlying data relative to the credit cycle.
Moreover, ETPMs are often required for use over time periods longer than the widely published one-year time horizon. While ETPMs can be constructed over any time horizon, longer time horizon calculations typically reduce sample size, thereby exacerbating idiosyncratic effects in proportion to less idiosyncratic effects and subsequently generating an ETPM with distorted values. Using the aforementioned smoothing techniques may help to reduce the distortions, but such smoothing techniques do not generate a matrix that will accurately predict transition probabilities for an obligor over a multi-year time horizon. Accordingly, many lenders use standard methods of applying one-year ETPMs iteratively, or more specifically, multiplying the one-year ETPM by itself for a discrete number of periods. Such a matrix raised to a specific power corresponding to the number of periods generates probability values for rating transition drift over multi-year horizons. One of the consequences of this method is that in practice, as the time horizon increases, an estimation “bias” induced by shortages in sample sizes is introduced into generation of the TPMs. Such estimation “bias” may be propagated throughout the entire matrix and may potentially undermine the validity and usefulness of these ETPMs. For example, monotonicity and/or smoothness of the resultant ETPM may not meet predetermined standards.
At least one known use of TPMs is described in a technical document entitled Credit Metrics™ by J.P. Morgan & Co., Incorporated (1997). Credit Metrics™ describes an approach of working backwards from a cumulative default table to create an implied transition matrix. Specifically, the Credit Metrics™ document describes creating a transition matrix using a least-squares fit to the cumulative default rates. Credit Metrics™, however, only describes using a simple least-square function for measuring a “fit” to historical data. Credit Metrics™ does not describe using any other functions, and as discussed below, a simple least-square function does not include all of the desired properties for generating an algorithm that optimizes the “fit” to historical data. In addition, Credit Metrics™ only describes fitting the cumulative default rates, and does not describe fitting the whole TPM. The approach described in Credit Metrics™ does not allow for adjusting a desired area in a TPM (e.g., upgrade/downgrade, default, volatility), it does not describe time weights, and it does not mention a technique for solving a large scale problem such as a 23×23 matrix.
Accordingly, it would be desirable to provide a process and/or a system that enables a lender to generate a TPM that more accurately models historical data such as obligors' credit ratings and credit migrations over a period of time, and more accurately predicts a future migration of an obligor's credit rating over a multi-year period of time.